Question

If the dimensions of a cuboid are in the ratio 1:2:3 and its total surface area is 88m ^ 2 , then its volume is
(a) 48m ^ 3
(b) 44m ^ 2
(c) 40m ^ 2
(d) 36m ^ 2​

Answer 1

Answer:

• Option (a) 48 m³ is the correct answer.

Step-by-step explanation:

Given:

• Dimensions of a cuboid are in the ratio 1:2:3 and its total surface area is 88 m²

To Find:

• Volume of cubiod.

Solution:

Let,

• Length of cubiod = 1x
• Breadth of cubiod = 2x
• Height of cubiod = 3x

TSA of cubiod = 88 m²

➛2(lb + bh + hl) = 88

➛2(2x² + 6x² + 3x²) = 88

➛2× 11x² = 88

➛11x² = 88/2

➛11x² = 44

➛x² = 44/11

➛x² = 4

➛x = 2 m

Hence,

• Length of cubiod = 1x = 2 m
• Breadth of cubiod = 2x = 4 m
• Height of cubiod = 3x = 6 m

Now,

• Volume of cubiod = L × B × H
• Volume of cubiod = 2 × 4 × 6
• Volume of cubiod = 48 m³

Hence,

• Volume of cubiod is 48 m³

Answer 2

Step-by-step explanation:

Given the ratio of the dimensions = 1:2:3.

Let the sides be x, 2 x, 3 x.

Total surface area of a cuboid =2( lb + bh + hl )

=2(x×2x + 2x×3x + x×3x)

$\\ \rm\Rightarrow 2\left(2 x^{2}+6 x^{2}+3 x^{2}\right)=88$

$\rm\Rightarrow 22 x^{2}=88$

$\text{\( \rm\Rightarrow x^{2}=4 m \) or \( \rm x=2 m \)}$

Hence, the sides are 2 m , 4 m and 6 m Therefore, volume

$\text{\( \rm =2 \times 4 \times 6=48 m ^{3} \).}$

$\\ \pmb{\boxed{\sf (A) \: \: 48 m ^{3} }}$